Research on Dynamic Modeling and Distributed Cooperative Control Method of Dumbbell-Shaped Spacecraft

Abstract

Purpose

To suppress the vibration of dumbbell-shaped spacecraft by combining distributed cooperative control (DCC) and component synthesis vibration suppression (CSVS).

Methods

The dumbbell-shaped spacecraft is divided into control sub-modules, and the dynamic model for distributed control is established according to Newton–Euler method and Lagrange’s equations of second kind; The distributed controller is designed by combining graph theory and consistency theory, and the stability of the closed-loop system is analyzed based on Lyapunov theory; CSVS + DCC method is proposed to suppress the vibration of dumbbell spacecraft. Finally, numerical simulation is used to verify the superiority and effectiveness.

Results

The large angle attitude maneuver of dumbbell spacecraft can be completed by CSVS + DCC method. Compared with bang-bang control, the stabilization time is shortened by 25.76%, and the vibration amplitude at the center of mass of the system is reduced by 53.06%.

Conclusion

The vibration of dumbbell spacecraft can be actively suppressed by CSVS + DCC active vibration suppression.

Appendices

Appendix 1

Equation (6), the simplification process applies the vector first relation as follows:

$$\int_B {{{\varvec{r}}} \times \left( {{\dot{\varvec{\omega }}} \times {{\varvec{\rho}}}} \right)} dm = \underline {{\varvec{e}}}^T \int_B {\left( {\underline{\rho}^T \underline{r} \underline{E} - \underline{\rho} \ \underline{r}^T } \right)} dm \cdot {\dot{\varvec{\omega }}}$$

(54)

When ${\varvec{r = \rho }}$, the vector first relation was transformed into:

$$\int_B {{{\varvec{r}}} \times \left( {{\dot{\varvec{\omega }}} \times {{\varvec{r}}}} \right)} dm = {\mathbb{J}} \cdot {\dot{\varvec{\omega }}}$$

(55)

Appendix 2

Equation (6), the second relation of vector applied in simplification process is as follows:

$$\int_B {{{\varvec{r}}} \times \left[ {{{\varvec{\omega}}} \times \left( {{{\varvec{\omega}}} \times {{\varvec{r}}}} \right)} \right]dm} = {{\varvec{\omega}}} \times {\mathbb{J}} \cdot {{\varvec{\omega}}}$$

(56)

Appendix 3

$$\begin{aligned} \underline{H}_{\Sigma} & = \int_A {\left( {{{\varvec{\zeta}}}_a + {{\varvec{\varDelta}}}_a + {{\varvec{r}}}_{o_a } + {{\varvec{\rho}}}_a } \right) \times \left[ {\underline {\beta}_1^1 + \left( {r_{o_a }^{ \times T} + \underline{\rho}_a^{ \times T} } \right)\underline {\beta}_2^1 } \right]} dm \\ & \quad + \int_C {\left( {{{\varvec{\zeta}}}_c + {{\varvec{\varDelta}}}_c + {{\varvec{r}}}_{o_c } + {{\varvec{\rho}}}_c } \right) \times \left[ {\underline {\beta}_3^{n_e } + \left( {\underline r_{o_c }^{ \times T} + \underline{\rho}_c^{ \times T} } \right)\underline {\beta}_4^{n_e } } \right]} dm \\ & \quad + \sum_{e = 1}^{n_e } {\int_e {\left( {{{\varvec{\zeta}}}_e + {{\varvec{\rho}}}_e + {{\varvec{\delta}}}_e } \right)} } \times \left( {\underline C_{me} \underline N^e \underline P^e } \right)dm. \\ \end{aligned}$$

(57)